Dr. Sudoku Prescribes: Median Link

Thomas Snyder (aka Dr. Sudoku) is a two-time World Sudoku Champion and five-time US Puzzle Champion, as well as the author of several books of puzzles. His puzzles are hand-crafted, with artistic themes, serving as a kind of “cure for the common sudoku.” Each week he posts a new puzzle on his blog, The Art of Puzzles. This week Doctor Sudoku starts to experiment with a new loop-drawing puzzle from Japan.
I really like simple loop puzzle types and ran into this fairly novel idea recently in some of Nikoli’s magazines (first debuting in #126). As I do with new designs in that magazine where I can’t read the Japanese instructions, I tried for awhile to look at example puzzles to figure out what was going on. This time Doctor Sudoku couldn’t prescribe the rules, and I reluctantly turned to a translation to get a sense for what was happening. I discovered a puzzle type that — while generally easy — has an interesting feel as far as loop puzzles go. This week I figured I’d explore the construction of the basic type as presented in Nikoli’s magazines before I take some steps to vary the formula and change the rules to make a more interesting solve space in the future. I find slight coloring of the grid helps emphasize the different tiles so this is the only change in formatting that I’ve made to Nikoli’s style.
Nikoli’s title メジリンク roughly translates to Median Link which is the name I’ll be using for it.
Rules: Draw a single closed loop that does not intersect itself using just the dotted lines of the grid. Each (colored) tile of area N must have a total length of unused dotted segments of exactly N.
Example:

Puzzle 1:

Puzzle 2: